On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations

A quasi-Newton algorithm for large-scale nonlinear equations

In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i) a conjugate gradient (CG) algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm's initial point does not have any restrictions; (ii) a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algor...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

Inexact Quasi-Newton methods for sparse systems of nonlinear equations

In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a Quasi-Newton method combined with a p block iterative row-projection linear solver of Cimmino-type, 1 p n: Under weak regularity conditions for F; it is proved that this Inexact Quasi-Newton method has a local, linear convergence in the energy norm induced by the precondit...

New quasi-Newton method for solving systems of nonlinear equations

In this paper, we propose the new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but it is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n) arithmetic operations per iteration in cont...

A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations

The present paper deals with fifth order convergent Newton-type with and without derivative iterative methods for estimating a simple root of nonlinear equations. The error equations are used to establish the fifth order of convergence of the proposed iterative methods. Finally, various numerical comparisons are made using MATLAB to demonstrate the performence of the developed methods.